Problem: Reduce to lowest terms: $- \dfrac{5}{6} \div \dfrac{2}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{2}{9}$ is $ \dfrac{9}{2}$ Therefore: $ - \dfrac{5}{6} \div \dfrac{2}{9} = - \dfrac{5}{6} \times \dfrac{9}{2} $ $ \phantom{- \dfrac{5}{6} \times \dfrac{9}{2}} = \dfrac{-5 \times 9}{6 \times 2} $ $ \phantom{- \dfrac{5}{6} \times \dfrac{9}{2}} = \dfrac{-45}{12} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{-45}{12} = \dfrac{-45 \div 3}{12 \div 3} = -\dfrac{15}{4} $